Stirling numbers are a set of mathematical numbers that count the ways to partition a set of objects. There are two types: Stirling numbers of the first kind, which count permutations with a specific number of cycles, and Stirling numbers of the second kind, which count ways to partition a set into non-empty subsets. These numbers have applications in combinatorics, algebra, and number theory. They help in solving problems related to arrangements and groupings, making them useful in various fields, including computer science and statistics.